In 15 1/2" by 10 1/2" jelly-roll pan, toss onion and tomatoes with oil until coated; arrange in single layer. Broil 12 to 15 minutes or until onion is brown and tomatoes begin to burst, stirring once. Remove from broiler and cool in pan. Reset oven control to 200°F. Remove peppers from foil; peel off skin and discard. Remove and discard stems and seeds; finely chop peppers.

Prepare quesadillas: On large work surface, arrange 8 tortillas in single layer. Divide Monterey Jack, cilantro, and chopped peppers among tortillas. Top with remaining tortillas.

Heat 10-in. skillet on medium until hot. Place one assembled quesadilla in skillet and cook 1 to 3 minutes or until bottom browns. Carefully turn and cook 1 to 3 minutes or until bottom browns. Transfer to clean large cookie sheet and place in oven. Repeat until all quesadillas are cooked and kept warm in oven.